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Arundeep
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DIVISIBILITY BY THIRTEEN : Osculator for 13 is 4 (See note). But this time our osculator is not negative (as in case of 7). It is 'one-more' osculator. So, the working will be different now. This can be seen in the following examples.Ex 1 : Is 143 divisible by 13 ? Soln : 14 3 : 14 + 3 x 4 = 26 Since 26 is divisible by 13, the number 143 is also divisible by 13. or, This working may further be simplified as Step I : 1 4 3 16 [4 x 3 (from 143) + 4 (from 143)] Step II: 1 4 3 26/16 [4 x 6 (from 16) +1 ( from 16) +1 ( from 143) = 26] As 26 is divisible by 13, the number is also divisible by 13. Note : The working of second method is also very systematic. At the same time it is more acceptable because it has less writing work. Ex 2: Check the divisibility of 24167 by 13. 2 4 1 6 7 26/6/20/34 [4x7 (from 24167) +6 ( from 24167)= 34] [4x4 (from 3 4) +3 (from 34) +1 (from 24167) = 20] [4x0 (from 20) +2 (from 20) +4 (from 24167) = 6] [4x6 (from 6) +2 (from 24167) = 26] Since 26 is divisible by 13 the number is also divisible by 13. Remark : Have you understood tbc working ? If Your answer is no, we suggest you to go through each step carefully. This is very simple and systematic calculation. Ex 3: Check the divisibility of 6944808 by 13. Soln : 6 9 4 4 8 0 8 39/18/12/41/19/32 4x8+0 = 32 4x2+3+8 = 19 4x9+1+4 = 41 4x1+4+4 = 12 4x2+1+9 = 18 4x8+1+6 = 39 Since 39 is divisible by 13, the given number is divisible by 13. Note : (1) This method is applicable for "one-more" osculator only. So we can't use this method in the case of 7. (2) This is a one-line method and you don't need to write the calculations during exams. These are given merely to make you understand well. |